Finite Group Databasebeta

← C103×#8907 #39914182

Subgroups — C103×#8907 #39914182

Order 26368.

376 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×M16×C103C211yesmaximal, characteristic
2C103×#1950C211yesmaximal, characteristic
3C103×#1567C211yesmaximal, characteristic
4C103×#1487C211yesmaximal, characteristic
5C2×Q8⋊C8×C103C211yesmaximal, characteristic
6C103×#1301C211yesmaximal, characteristic
7C103×#1278C211yesmaximal, characteristic
8C2×C4×Q8×C103C2211yescharacteristic
9#446×C103—21no—
10#446×C103—22no—
11C8×Q8×C103—21no—
12#431×C103C2211yescharacteristic
13C2×#108×C103—21no—
14#423×C103—21no—
15#423×C103C2211yescharacteristic
16#423×C103C2211yescharacteristic
17C2×C4⋊C8×C103C2211yescharacteristic
18C4×M16×C103—21no—
19C4×M16×C103C2211yescharacteristic
20C2×C4×C8×C103C2211yescharacteristic
21#341×C103—21no—
22#335×C103—22no—
23Q8⋊C8×C103—21no—
24Q8⋊C8×C103—21no—
25Q8⋊C8×C103C411yescharacteristic
26Q8⋊C8×C103C411yescharacteristic
27Q8⋊C8×C103C411yescharacteristic
28Q8⋊C8×C103C411yescharacteristic
29C22×Q8×C103Q811yescharacteristic
30C2×M16×C103—21no—
31C2×M16×C103—21no—
32C2×M16×C103D411yescharacteristic
33C2×M16×C103D411yescharacteristic
34C22×C8×C103—21no—
35C22×C8×C103—21no—
36C4×Q8×C103—21no—
37C4×Q8×C103—21no—
38C4×Q8×C103C2×C411yescharacteristic
39C4×Q8×C103C2×C411yescharacteristic
40C4×Q8×C103D411yescharacteristic
41C4×Q8×C103D411yescharacteristic
42C2×C4⋊C4×C103—21no—
43C2×C4⋊C4×C103Q811yescharacteristic
44C2×C42×C103—21no—
45C2×C42×C103C2311yescharacteristic
46#108×C103—42no—
47C4⋊C8×C103—22no—
48C4⋊C8×C103—22no—
49C4⋊C8×C103—21no—
50C4⋊C8×C103—21no—
51C4⋊C8×C103—21no—
52C4⋊C8×C103—21no—
53C4⋊C8×C103—21no—
54C4⋊C8×C103C2×C411yescharacteristic
55C4⋊C8×C103C2×C411yescharacteristic
56C4⋊C8×C103D412yes—
57C22⋊C8×C103—21no—
58#97×C103—22no—
59#97×C103—21no—
60C4×C8×C103—22no—
61C4×C8×C103—21no—
62C4×C8×C103—21no—
63C4×C8×C103—21no—
64C4×C8×C103C2×C411yescharacteristic
65C4×C8×C103C2×C411yescharacteristic
66C2×Q8×C103—21no—
67C2×Q8×C103—22no—
68C2×Q8×C103—41no—
69C2×Q8×C103C4⋊C411yescharacteristic
70C2×Q8×C103C4⋊C411yescharacteristic
71C22×C4×C103—21no—
72C22×C4×C103—21no—
73C22×C4×C103C2×D411yescharacteristic
74C22×C4×C103C2×Q811yescharacteristic
75C22×C4×C103#4111yescharacteristic
76M16×C103—21no—
77M16×C103—21no—
78M16×C103—21no—
79M16×C103—41no—
80M16×C103—41no—
81M16×C103—41no—
82M16×C103—41no—
83M16×C103Q1612yes—
84C2×C8×C103—21no—
85C2×C8×C103—21no—
86C2×C8×C103—21no—
87C2×C8×C103—21no—
88C2×C8×C103—21no—
89C2×C8×C103—21no—
90C2×C8×C103—22no—
91C2×C8×C103—42no—
92C2×C8×C103—41no—
93C2×C8×C103—41no—
94C2×C8×C103—41no—
95C2×C8×C103—41no—
96C4⋊C4×C103—21no—
97C4⋊C4×C103—21no—
98C4⋊C4×C103—21no—
99C4⋊C4×C103—21no—
100C4⋊C4×C103—21no—
101C4⋊C4×C103C4⋊C411yescharacteristic
102C4⋊C4×C103C4⋊C411yescharacteristic
103C42×C103—21no—
104C42×C103—21no—
105C42×C103—21no—
106C42×C103—21no—
107C42×C103C22×C411yescharacteristic
108C42×C103C2×D411yescharacteristic
109C42×C103C2×D411yescharacteristic
110C42×C103#4111yescharacteristic
111C23×C103C22⋊Q811yescharacteristic
112Q8×C103—21no—
113Q8×C103—21no—
114Q8×C103—21no—
115Q8×C103—42no—
116Q8×C103#10812yescomplemented
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—41no—
124C2×C4×C103—42no—
125C2×C4×C103—81no—
126C2×C4×C103C2×C4⋊C411yescharacteristic
127C2×C4×C103C4×D411yescharacteristic
128C2×C4×C103C4×D411yescharacteristic
129C2×C4×C103#12011yescharacteristic
130C2×C4×C103C22⋊Q811yescharacteristic
131C2×C4×C103#12311yescharacteristic
132C2×C4×C103C2×Q1611yescharacteristic
133C2×C4×C103#13511yescharacteristic
134C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C103#13711yescharacteristic
136C8×C103—22no—
137C8×C103—22no—
138C8×C103—41no—
139C8×C103—41no—
140C8×C103—41no—
141C8×C103—41no—
142C8×C103—42no—
143C8×C103—81no—
144C8×C103—81no—
145C22×C103—21no—
146C22×C103—21no—
147C22×C103#38511yescharacteristic
148C22×C103#47711yescharacteristic
149C22×C103#47911yescharacteristic
150C4×C103—21no—
151C4×C103—22no—
152C4×C103—21no—
153C4×C103—21no—
154C4×C103—41no—
155C4×C103—41no—
156C4×C103—41no—
157C4×C103C2×#10811yescharacteristic
158C4×C103#43011yescharacteristic
159C4×C103C4×Q1611yescharacteristic
160C4×C103#44011yescharacteristic
161C4×C103#44911yescharacteristic
162C4×C103#45111yescharacteristic
163#8907C10311yesmaximal, characteristic, direct product factor, Sylow
164C2×C103—21no—
165C2×C103—21no—
166C2×C103#185511yescharacteristic
167C2×C103#186111yescharacteristic
168C2×C103#186311yescharacteristic
169Q8×M16C2×C10311yescharacteristic
170#1950C2×C10311yescharacteristic
171#1567C2×C10311yescharacteristic
172#1487C2×C10311yescharacteristic
173C2×Q8⋊C8C2×C10311yescharacteristic
174#1301C2×C10311yescharacteristic
175#1278C2×C10311yescharacteristic
176C103#890711yescharacteristic, direct product factor, Sylow
177C2×C4×Q8C22×C10311yescharacteristic
178#446—21no—
179#446—22no—
180C8×Q8—21no—
181#431C22×C10311yescharacteristic
182C2×#108—21no—
183#423—21no—
184#423C22×C10311yescharacteristic
185#423C22×C10311yescharacteristic
186C2×C4⋊C8C22×C10311yescharacteristic
187C4×M16—21no—
188C4×M16C22×C10311yescharacteristic
189C2×C4×C8C22×C10311yescharacteristic
190#341—21no—
191#335—22no—
192Q8⋊C8—21no—
193Q8⋊C8—21no—
194Q8⋊C8C4×C10311yescharacteristic
195Q8⋊C8C4×C10311yescharacteristic
196Q8⋊C8C4×C10311yescharacteristic
197Q8⋊C8C4×C10311yescharacteristic
198C22×Q8Q8×C10311yescharacteristic
199C2×M16—21no—
200C2×M16—21no—
201C2×M16D4×C10311yescharacteristic
202C2×M16D4×C10311yescharacteristic
203C22×C8—21no—
204C22×C8—21no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8C2×C4×C10311yescharacteristic
208C4×Q8C2×C4×C10311yescharacteristic
209C4×Q8D4×C10311yescharacteristic
210C4×Q8D4×C10311yescharacteristic
211C2×C4⋊C4—21no—
212C2×C4⋊C4Q8×C10311yescharacteristic
213C2×C42—21no—
214C2×C42C23×C10311yescharacteristic
215#108—42no—
216C4⋊C8—22no—
217C4⋊C8—22no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8C2×C4×C10311yescharacteristic
224C4⋊C8C2×C4×C10311yescharacteristic
225C4⋊C8D4×C10312yes—
226C22⋊C8—21no—
227#97—22no—
228#97—21no—
229C4×C8—22no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—21no—
233C4×C8C2×C4×C10311yescharacteristic
234C4×C8C2×C4×C10311yescharacteristic
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8C4⋊C4×C10311yescharacteristic
239C2×Q8C4⋊C4×C10311yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×D4×C10311yescharacteristic
243C22×C4C2×Q8×C10311yescharacteristic
244C22×C4#41×C10311yescharacteristic
245M16—21no—
246M16—21no—
247M16—21no—
248M16—41no—
249M16—41no—
250M16—41no—
251M16—41no—
252M16Q16×C10312yes—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—22no—
260C2×C8—42no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4C4⋊C4×C10311yescharacteristic
271C4⋊C4C4⋊C4×C10311yescharacteristic
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42C22×C4×C10311yescharacteristic
277C42C2×D4×C10311yescharacteristic
278C42C2×D4×C10311yescharacteristic
279C42#41×C10311yescharacteristic
280C23C22⋊Q8×C10311yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—42no—
285Q8#108×C10312yescomplemented
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4C2×C4⋊C4×C10311yescharacteristic
296C2×C4C4×D4×C10311yescharacteristic
297C2×C4C4×D4×C10311yescharacteristic
298C2×C4#120×C10311yescharacteristic
299C2×C4C22⋊Q8×C10311yescharacteristic
300C2×C4#123×C10311yescharacteristic
301C2×C4C2×Q16×C10311yescharacteristic
302C2×C4#135×C10311yescharacteristic
303C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
304C2×C4#137×C10311yescharacteristic
305C8—22no—
306C8—22no—
307C8—41no—
308C8—41no—
309C8—41no—
310C8—41no—
311C8—42no—
312C8—81no—
313C8—81no—
314C22—21no—
315C22—21no—
316C22#385×C10311yescharacteristic
317C22#477×C10311yescharacteristic
318C22#479×C10311yescharacteristic
319C4—21no—
320C4—22no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4C2×#108×C10311yescharacteristic
327C4#430×C10311yescharacteristic
328C4C4×Q16×C10311yescharacteristic
329C4#440×C10311yescharacteristic
330C4#449×C10311yescharacteristic
331C4#451×C10311yescharacteristic
332C2—21no—
333C2—21no—
334C2C103×#185511yescharacteristic
335C2C103×#186111yescharacteristic
336C2C103×#186311yescharacteristic
subgroupG/H
centerC2×C4×C103#120
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
socleC22×C103#385
prime radicalC23×C103C22⋊Q8
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
116. Q8×C103#108semidirect
163. #8907C103direct (N × H)
176. C103#8907direct (N × H)
285. Q8#108×C103semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
Q8×M16×C1032
C103×#19502
C103×#15672
C103×#14872
C2×Q8⋊C8×C1032
C103×#13012
C103×#12782
#8907103